Necessary and sufficient conditions for Pareto optimality in differential games

P.V. Reddy, J.C. Engwerda

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Abstract

In this article we derive necessary and sufficient conditions for the existence of Pareto optimal solutions for an N player cooperative infinite horizon differential game. Firstly, we write the problem of finding Pareto candidates as solving N constrained optimal control subproblems. We derive some weak conditions which entail one to find all Pareto candidates by solving a weighted sum optimal control problem. We observe that these conditions are related to transversality conditions of the associated subproblems. Furthermore, we derive sufficient conditions under which candidate Pareto solutions are indeed obtained by solving a weighted sum optimal control problem. We consider games defined by nonautonomous and discounted autonomous systems. The obtained results are used to analyze the regular indefinite linear quadratic infinite horizon differential game. For the scalar case we devise an algorithm to find all the Pareto optimal solutions.
Original languageEnglish
Title of host publicationProceedings of the 14th International Symposium on Dynamic Games and Applications (ISDG2010)
EditorsP. Cardaliaguet, R. Cressman
Place of PublicationBasel
PublisherBirkhauser
Publication statusPublished - 2011

Publication series

NameAnnals of the International Society of Dynamic Games

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Reddy, P. V., & Engwerda, J. C. (2011). Necessary and sufficient conditions for Pareto optimality in differential games. In P. Cardaliaguet, & R. Cressman (Eds.), Proceedings of the 14th International Symposium on Dynamic Games and Applications (ISDG2010) (Annals of the International Society of Dynamic Games). Birkhauser. http://cse.stfx.ca/~isdg2010/sub/FILESP/p50.pdf